%problem 9.3 Andrew Seta
xa=[1:500];
xb=(120+1.1*xa)/10;
plot (xa,xb)
hold on
xb=(174+2*xa)/17.4;
plot (xa,xb)
grid on
xa =
405
xb=(120+1.1*xa)/10
xb =
56.5500
xb=(174+2*xa)/17.4
xb =
56.5517
xb=xb
%Part B
% Since the slopes were so close the condition of
ESM/AOE 2074
Computational Methods
Day 13
February 16, 2011
Note from last time:
MATLAB logical operators | and & are shortcircuit operators. In the expression:
A | B
B is only evaluated if A is not true. If A is true, there
is no need to evaluate B. Simi
MATLAB Command Window
MATLAB desktop keyboard shortcuts, such as Ctrl+S, are now customizable.
In addition, many keyboard shortcuts have changed for improved consistency
across the desktop.
To customize keyboard shortcuts, use Preferences. From there, you
%Problem 9.12 Andrew Seta
%Solved a second order linear homogenous differential equation to get the
%equation y=C[1]*exp^.653*x + C[2]*exp^-.153*x
clear
clc
%c[0] = c[1]*exp^.653*x[1]+c[2]*exp^-.153*x[1];
%c[10]= c[1]*exp^.653*x[2]+c[2]*exp^-.153*x[2];
a=
AOE 2204 Dr. W. L. Neu
Pressure and Forces in Static Fluids
Pressure variation
Consider an infinitesimal element with dimensions dx,dy,dz in equilibrium in a static
fluid. Pressure, p, acts inward on all faces of the element. The element has weight dW.
Th
Stability of Floating Bodies
Body completely submerged
The buoyancy force, FB, acting at B, is
equal and opposite to the weight, W,
acting at the center of gravity, G.
As sub rolls, the position of center of buoyancy, B, relative to the sub, does not
chan
AOE 2204 Dr. W. L. Neu
Stability of Floating Bodies
1. Body completely submerged
Consider a submarine,
In Equilibrium
Rolled
FB
B
G
FB
B
G
W
W
In equilibrium, the buoyancy force, FB, acting at B, is equal and opposite to the weight,
W, acting at the cente
Thermohaline Circulation
Thermohaline circulation is responsible for most of the vertical mixing in the ocean.
It is driven by density differences causing one water mass to sink and slide under another,
less dense mass. The density characteristics of a wa
Properties of Seawater
All properties depend on temperature, salinity and pressure so we will look at these
first.
Temperature
Look at the figure of typical temperature profiles. You see a surface layer or mixed
layer in the first few tens of meters of de
AOE 2204 Dr. W. L. Neu
Physical Oceanography
Physical Oceanography References (and sources of figures)
Less Mathematical:
Oceanography: A View of the Earth, Gross, M.G., Prentice-Hall, 1982
Essentials of Oceanography, Thurman, H.V., Prentice-Hall, 1996
Mo
AOE 2204 Dr. W. L. Neu
Physical Oceanography
Physical Oceanography References (and sources of figures)
Less Mathematical:
Oceanography: A View of the Earth, Gross, M.G., Prentice-Hall, 1982
Essentials of Oceanography, Thurman, H.V., Prentice-Hall, 1996
Mo
AOE 2204 Dr. W. L. Neu
Hydrodynamics
Viscosity
Viscosity is the property of a fluid which gives rise to shear stress when the fluid moves.
Assume the fluid to be composed of layers moving relative to one another (this is called
laminar flow).
If one layer
Hydrodynamics
Viscosity
Viscosity is the property of a fluid which gives rise to shear stress when the fluid
moves. Assume the fluid to be composed of layers moving relative to one another
(this is called laminar flow).
If one layer moves faster than the
Manometry
pM = a + A d1 = N = atm + Hg d 2
p
p
p
pa = patm + Hg d 2 A d1
pa patm + Hg d 2
AOE 2204 Intro to Ocean Eng
Dr. W. L. Neu
1
pa + A d3 + Hg d 2 B d1 =
pb
pb pa = A d3 + Hg d 2 B d1
In tank A we have water, specific weight of 9806 N/m3 and
in B t
Basic Definitions
Ship = big
Boat = small
Bow = front (fore, forward)
Port = left
(fuzzy distinction)
Stern = back (aft)
Starboard = right (facing forward)
(Bow)stem = leading edge, often a single piece
Keel = forms the centerline along the bottom
Beam =
Test I, Solution
[1] Parametric equations for L1 are
x = 1 + 2t,
y = t,
z = 1 + 3t,
< t <
The intersection point can be expressed by
x = 1 + 2 t ,
y = t ,
z = 1 + 3t
for some t . To satisfy the plane equation
1 + 2t + t + 2(1 + 3t ) = 2
and t = 1/9. So
Mat h 22 24 Mu ltiva ri a ble C alc ul u s S ec. 10 .6: C yli n de rs a n d Q ua d ratic Su r fac e s
I.
Revi e w o f Co ni c Sect io n s
A. Parabolas
y = x2
or
x = y2
x 2 y2
+
=1
B. Ellipses
a2 b2
C. Hyperbolas
If
a=b, then we have a circle.
x 2 y2
y2 x
M ath 2224 Multivariable Calculus S ec. 10.5: Lines and Planes in Space
= for all
Defn = definition
= perpendicular
fn = function
st = such that
Abbreviations: wrt = with respect to
= therefore
soln = solution
pt = point
=is an element of
I.
= there e
Solutions Quiz 3
[1]
22rcos( )rsin( )
2/(2cos( )+sin( )
/2
r3 cos()sin() dz dr d
0
0
0
[2]
4r
1
2
r dz dr d = 5/6
r 2 +2
0
0
[3]
2
2
/2
r
0
0
z2r
dz dr d
r2 + z 2
[4]
/2
/2
2sin()
4 sin3 () d d d
/4
0
0
[5]
2
/4
4sec()
5 sin3 ()cos()sin()cos() d d d
Quiz III, Math 2224
Due Date: November 9, 2010
Late papers will NOT be accepted. You should not get any help from
other people. Study class notes rst.
[1] Let D be the solid tetrahedron in the rst octant bounded by the coordinate
planes and the plane 2x +
Quiz 2, Math 2224
Due Date: October 7, 2010
Late papers will not be accepted. You should not get any help from
other people.
Guesswork will not be accepted. All answers must be given in precise
numbers. Do not use a calculator.
[1] Let w = y ln(xz + 3) +
Homework No. 12 Due Thursday, 10/13
(1) 4.192
Ans: 8.82 ksi in tension and 14.71 ksi in compression
(2) 4.18
Ans: 4.11 kipin
(3) 4.19
Ans: 177.8 kNm
(4) Two equal and opposite moments of magnitude M = 25 kNm are applied to the
straight beam as shown. Dete
Homework No. 11 Due Tuesday, 10/11
(1) For the cross-section shown in Fig. P4.10 on page 238 in the book, locate the centroid
and then calculate the moment of inertia with respect to the horizontal centroidal axis.
Ans: 25 mm above the base, I = 512.5 103
Homework No. 10 Due Tuesday, 10/4
(1) 3.28
Ans: (a) 20.1 mm (b) 26.9 mm (c) 36.6 mm
(2) 3.158
Ans: 36.1 mm
(3) 3.78
Ans: 4.90 Hz
(4) 3.79
Ans: 50.0 kW
(5) 3.52 Determine the largest torque T that can be applied on the composite shaft and the
angle that en